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Geometry & Topology Seminar

Title: Bergman-Szegő kernel asymptotics in weakly pseudoconvex finite type cases
Speaker: Nikhil Savale (Universität zu Köln, Germany)
Date: 30 November 2022
Time: 4:00 pm
Venue: Microsoft Teams (online) (Joint with the APRG Seminar)

We construct a pointwise Boutet de Monvel-Sjostrand parametrix for the Szegő kernel of a weakly pseudoconvex three dimensional CR manifold of finite type assuming the range of its tangential CR operator to be closed; thereby extending the earlier analysis of Christ. This particularly extends Fefferman’s boundary asymptotics of the Bergman kernel to weakly pseudo-convex domains in dimension two. Next we present an application where we prove that a weakly pseudoconvex two dimensional domain of finite type with a Kähler-Einstein Bergman metric is biholomorphic to the unit ball. This extends earlier work of Fu-Wong and Nemirovski-Shafikov. Based on joint works with C.Y. Hsiao and M. Xiao.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 08 Dec 2022